Tannakization of quasi-categories and monadic descent

Abstract

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ and a left adjoint symmetric monoidal fiber functor to ${\mathrm{Mod}}_A^{\otimes }$ for some ${\mathbb{E}}_{\infty }$-ring $A$, one can construct a derived group scheme $G$ of monoidal automorphisms of this functor. The left adjoint fiber functor also induces a monad on $\mathcal{C}$. Under some finiteness hypothesis on the fiber functor, we show there is a comparison functor from the category of representations of $G$ to the descent category of the induced monad on $\mathcal{C}$.

References in corpus (3)

• Higher Topos Theory
• Some Higher Coalgebra
• Galois Descent for Real Spectra